Rather than inserting your elements directly into the queue, wrap each element in a tuple, where the first element in the tuple is the desired sorting key. Tuples are sorted by in order of their elements (i.e., first element is compared first), hence why the sorting key needs to come first.
Regarding std::priority_queue: A user-provided Compare can be supplied to change the ordering, e.g. using std::greater<T> would cause the smallest element to appear as the top(). Since std::less<T> is the default template argument to the Compare template parameter, it is already a max heap by default. If you want a min heap instead (what the quote above suggest), pass std::greater<T> instead of std::less<T> as the template argument. To summarize: Max Heap: pass std::less<T> (this is the default template … Read more